Estimation of the efficiency of the method of hierarchical reconstruction for the problem of the reconstruction of discrete scattering centers from projections

We study the actual problem of determining the maximal set for the set of points in $\mathbb R^3$ from the set of two-dimensional projections. This problem arises naturally in the applications of physical hydrodynamics for the optical diagnostics of real flows of liquid and gas by measuring the instantaneous rate fields in the volume of flow. We propose a method for reconstructing the given set and determining the sufficiency of the measurements for the uniqueness of a solution to the inverse problem for parallel and perspective projections. A statistical evaluation for the efficiency of the reconstruction method is obtained.